Expanding plane size while keeping existing vertices
Here's an alternate method that might be useful in some circumstances. In edit mode, select one of the vertices of the plane, and from the context menu of the snap tool (SHFT - S), select "Cursor to selected". Next, invert the selection (CTRL - I), to deselect the original vertex, and select the other three. Then set the pivot point to 3D cursor, extrude the selected vertices, and scale to the desired size.